Int. J. Contemp. Math. Sci., Vol. 1, 2006, no. 2, 53 - 66 Explicit representations of the edge cone of a graph Carlos E. Valencia 1 Instituto de Matem´ aticas Universidad Nacional Autonoma de M´ exico Circuito Exterior, Ciudad Universitaria M´ exico City, D.F., 04510, M´ exico cvalencia@math.unam.mx Rafael H. Villarreal 2 Departamento de Matem´ aticas Centro de Investigaci´ on y de Estudios Avanzados del IPN Apartado Postal 14–740 07000 M´ exico City, D.F. vila@esfm.ipn.mx Abstract Let G be an arbitrary graph. The main results are explicit representa- tions of the edge cone of G as a finite intersection of closed halfspaces. If G is bipartite and connected we determine the facets of the edge cone and present a canonical irreducible representation. Mathematics Subject Classification: Primary 05C50; Secondary 52B05 Keywords: bipartite graph, edge cone, facets, marriage problem 1 Edge cones In the sequel we use standard terminology and notation from graph theory and adopt [1] as our main reference. For the reader’s convenience, along the 1 The author was partially supported by CTIC-UNAM and SNI, M´ exico. 2 Partially supported by CONACyT grant 49251E and SNI, M´ exico.